Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,4,15,6}

Atlas Canonical Name {2,4,15,6}*1440

Overview

Group
SmallGroup(1440,5900)
Rank
5
Schläfli Type
{2,4,15,6}
Vertices, edges, …
2, 4, 30, 45, 6
Order of s0s1s2s3s4
30
Order of s0s1s2s3s4s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Non-Orientable
  • Flat

Quotients maximal quotients in bold

3-fold

5-fold

15-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := (1,2);;
s1 := ( 3, 5)( 4, 6)( 7, 9)( 8,10)(11,13)(12,14)(15,17)(16,18)(19,21)(20,22)(23,25)(24,26)(27,29)(28,30)(31,33)(32,34)(35,37)(36,38)(39,41)(40,42)(43,45)(44,46)(47,49)(48,50)(51,53)(52,54)(55,57)(56,58)(59,61)(60,62);;
s2 := ( 4, 5)( 7,19)( 8,21)( 9,20)(10,22)(11,15)(12,17)(13,16)(14,18)(23,43)(24,45)(25,44)(26,46)(27,59)(28,61)(29,60)(30,62)(31,55)(32,57)(33,56)(34,58)(35,51)(36,53)(37,52)(38,54)(39,47)(40,49)(41,48)(42,50);;
s3 := ( 3,27)( 4,30)( 5,29)( 6,28)( 7,23)( 8,26)( 9,25)(10,24)(11,39)(12,42)(13,41)(14,40)(15,35)(16,38)(17,37)(18,36)(19,31)(20,34)(21,33)(22,32)(43,47)(44,50)(45,49)(46,48)(51,59)(52,62)(53,61)(54,60)(56,58);;
s4 := (23,43)(24,44)(25,45)(26,46)(27,47)(28,48)(29,49)(30,50)(31,51)(32,52)(33,53)(34,54)(35,55)(36,56)(37,57)(38,58)(39,59)(40,60)(41,61)(42,62);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s1*s2, 
s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, s2*s3*s2*s3*s4*s3*s2*s3*s2*s3*s4*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(62)!(1,2);
s1 := Sym(62)!( 3, 5)( 4, 6)( 7, 9)( 8,10)(11,13)(12,14)(15,17)(16,18)(19,21)(20,22)(23,25)(24,26)(27,29)(28,30)(31,33)(32,34)(35,37)(36,38)(39,41)(40,42)(43,45)(44,46)(47,49)(48,50)(51,53)(52,54)(55,57)(56,58)(59,61)(60,62);
s2 := Sym(62)!( 4, 5)( 7,19)( 8,21)( 9,20)(10,22)(11,15)(12,17)(13,16)(14,18)(23,43)(24,45)(25,44)(26,46)(27,59)(28,61)(29,60)(30,62)(31,55)(32,57)(33,56)(34,58)(35,51)(36,53)(37,52)(38,54)(39,47)(40,49)(41,48)(42,50);
s3 := Sym(62)!( 3,27)( 4,30)( 5,29)( 6,28)( 7,23)( 8,26)( 9,25)(10,24)(11,39)(12,42)(13,41)(14,40)(15,35)(16,38)(17,37)(18,36)(19,31)(20,34)(21,33)(22,32)(43,47)(44,50)(45,49)(46,48)(51,59)(52,62)(53,61)(54,60)(56,58);
s4 := Sym(62)!(23,43)(24,44)(25,45)(26,46)(27,47)(28,48)(29,49)(30,50)(31,51)(32,52)(33,53)(34,54)(35,55)(36,56)(37,57)(38,58)(39,59)(40,60)(41,61)(42,62);
poly := sub<Sym(62)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s1*s2, s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, 
s2*s3*s2*s3*s4*s3*s2*s3*s2*s3*s4*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;